scholarly journals Atangana-Baleanu and Caputo-Fabrizio Analysis of Fractional Derivatives on MHD Flow past a Moving Vertical Plate with Variable Viscosity and Thermal Conductivity in a Porous Medium

2021 ◽  
Vol 6 (2) ◽  
pp. 493-509
Author(s):  
Dipen Saikia ◽  
Utpal Kumar Saha ◽  
Gopal Chandra Hazarika
Keyword(s):  
Thermal Conductivity ◽  
Porous Medium ◽  
Concentration Distribution ◽  
Fractional Derivatives ◽  
Vertical Plate ◽  
Variable Viscosity ◽  
Mhd Flow ◽  
Iteration Scheme ◽  
Physical Parameters ◽  
Similarity Transformations

In this paper, a numerical investigation is presented for non-integer order derivatives with Atangana-Baleanu (AB) and Caputo-Fabrizio (CF) fractional derivatives for the variable viscosity and thermal conductivity over a moving vertical plate in a porous medium two dimensional free convection unsteady MHD flow. The effects of radiation have also been considered. The governing partial differential equations along with the boundary conditions are changed to ordinary form by similarity transformations. Hence physical parameters show up in the equations and interpretations on these parameters can be achieved suitably.By using ordinary finite difference scheme the equations are discritized and developed in fractional form. These discritized equations are numerically solved by the approach based on Gauss-seidel iteration scheme. Some numerical strategies are used to find the values of AB and CF approaches on time by developing programming code in MATLAB. The effects of all the physical parameters involved in the problem on velocity, temperature and concentration distribution are compared graphically as well as in tabular form. The effects of each parameter are found to be prominent. We have observed a significant variation of values under different parameters using AB and CF approaches on velocity, temperature and concentration distribution with respect to time.

Unsteady Magnetohydrodynamics Slip Flow of Powell-Eyring Fluid with Microorganisms Over an Inclined Permeable Stretching Sheet

2021 ◽  
Vol 10 (1) ◽  
pp. 128-145
Author(s):  
Amala Olkha ◽  
Amit Dadheech
Keyword(s):  
Thermal Conductivity ◽  
Porous Media ◽  
Friction Coefficient ◽  
Stretching Sheet ◽  
Variable Viscosity ◽  
Slip Flow ◽  
Mhd Flow ◽  
Skin Friction Coefficient ◽  
Physical Parameters ◽  
Linear Nature

The unsteady MHD flow of Powell-Eyring fluid with microorganisms due to permeable extending surface which is also inclined, embedded in porous media is acknwledged. We have considered variable fluid property such as variable viscosity, thermal conductivity. For this perspective relevant transformations are exercised to reduce the governing PDE’s corresponding to momentum energy, mass and microorganisms’ profiles to system of ODE’s which are of non-linear nature and are numerically evaluated by MATLAB algorithm using Runge-kutta technique. Tabular annotations including pictorial presentations are comprehensively used to analyse effects caused by physical parameters concerning velocity, energy, mass and microorganisms.The present analysis focuses the study of unsteady MHD slip flow of Powell-Eyring fluid with microorganisms over an inclined permeable stretching sheet with slip conditions which is not avalaible in open literature beforehand. Rising unsteady parameter (A) decreases skin friction coefficient and reverse impact is shown on local Sherwood, Nusselt, and motile microorganisms’ number.

Temperature-dependent variable viscosity and thermal conductivity effects on non-Newtonian fluids flow in a porous medium

2022 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Ayegbusi Dami Florence
Keyword(s):  
Thermal Conductivity ◽  
Porous Medium ◽  
Iterative Method ◽  
Variable Viscosity ◽  
Newtonian Fluids ◽  
Physical Parameters ◽  
Relaxation Techniques ◽  
Temperature Profiles ◽  
Content Type ◽  
Spectral Relaxation

Purpose The purpose of this paper is to consider the simultaneous flow of Casson Williamson non Newtonian fluids in a vertical porous medium under the influence of variable thermos-physical parameters. Design/methodology/approach The model equations are a set of partial differential equations (PDEs). These PDEs were transformed into a non-dimensionless form using suitable non-dimensional quantities. The transformed equations were solved numerically using an iterative method called spectral relaxation techniques. The spectral relaxation technique is an iterative method that uses the Gauss-Seidel approach in discretizing and linearizing the set of equations. Findings It was found out in the study that a considerable number of variable viscosity parameter leads to decrease in the velocity and temperature profiles. Increase in the variable thermal conductivity parameter degenerates the velocity as well as temperature profiles. Hence, the variable thermo-physical parameters greatly influence the non-Newtonian fluids flow. Originality/value This study considered the simultaneous flow of Casson-Williamson non-Newtonian fluids by considering the fluid thermal properties to vary within the fluid layers. To the best of the author’s knowledge, such study has not been considered in literature.

Soret Effect on the Natural Convection From a Vertical Plate in a Thermally Stratified Porous Medium Saturated With Non-Newtonian Liquid

2013 ◽  
Vol 135 (3) ◽  
Author(s):  
M. Narayana ◽  
A. A. Khidir ◽  
P. Sibanda ◽  
P. V. S. N. Murthy
Keyword(s):  
Porous Medium ◽  
Differential Equations ◽  
Power Law ◽  
Vertical Plate ◽  
Variable Viscosity ◽  
Soret Effect ◽  
Linearization Method ◽  
Convection Flow ◽  
Physical Parameters ◽  
Transfer Coefficients

The paper highlights the application of a recent seminumerical successive linearization method (SLM) in solving highly coupled, nonlinear boundary value problem. The method is presented in detail by solving the problem of free convection flow due to a vertical plate embedded in a non-Darcy thermally stratified porous medium saturated with a non-Newtonian power-law liquid. Thermal-diffusion (Soret) and variable viscosity effects are taken into consideration. The Ostwald–de Waele power-law model is used to characterize the non-Newtonian behavior of the fluid. The governing partial differential equations are transformed into a system of ordinary differential equations and solved by SLM. The accuracy of the SLM has been tested by comparing the results with those obtained using the shooting technique. The effect of various physical parameters such as power-law index, Soret number, variable viscosity parameter, and thermal stratification parameter on the dynamics of the fluid is analyzed through computed results. Heat and mass transfer coefficients are also shown graphically for different values of the parameters.

scholarly journals Effects of variable viscosity and thermal conductivity on unsteady MHD flow of non-Newtonian fluid over a stretching porous sheet

2013 ◽  
Vol 17 (4) ◽  
pp. 1035-1047 ◽  
Author(s):  
Abdel-Gamal Rahman
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Thermal Conductivity ◽  
Porous Medium ◽  
Differential Equations ◽  
Newtonian Fluid ◽  
Variable Viscosity ◽  
Mhd Flow ◽  
Transverse Magnetic ◽  
Electrically Conducting

The unsteady flow and heat transfer in an incompressible laminar, electrically conducting and non-Newtonian fluid over a non-isothermal stretching sheet with the variation in the viscosity and thermal conductivity in a porous medium by the influence of an external transverse magnetic field have been obtained and studied numerically. By using similarity analysis the governing differential equations are transformed into a set of non-linear coupled ordinary differential equations which are solved numerically. Numerical results were presented for velocity and temperature profiles for different parameters of the problem as power law parameter, unsteadiness parameter, radiation parameter, magnetic field parameter, porous medium parameter, temperature buoyancy parameter, Prandtl parameter, modified Eckert parameter, Joule heating parameter , heat source/sink parameter and others. A comparison with previously published work has been carried out and the results are found to be in good agreement. Also the effects of the pertinent parameters on the skin friction and the rate of heat transfer are obtained and discussed numerically and illustrated graphically.

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